If you do a PhD by research it is always a great plus (for yourself and for your CV) if you can obtain independent funding (from a funding agency, not from your host university or the laboratory you will work in). Sometimes, if your host institution cannot fund you completely, it is the only way to survive. Funding sources will depend on the country you are aiming to go to, and the country of your citizenship.

Sources of information:

In principle, CSC at Jacobs should be able to advise you, and individual faculty members may have additional information.

The GrantsNet website maintained by the Howard Hughes Medical Institute (HHMI) and the American Association for the Advancement of Science (AAAS): http://www.grantsnet.org/.

Graduate scholarships in Germany:

In Germany, Masters programs at public universities are usually free but the university provides no salary. PhD students pay no tuition fee, either, and they are paid a salary from the investigator's grant.

DAAD Research Grants for Doctoral Candidates

(DAAD, German Academic Exchange Service)

Country:

Germany

Covers:

maintenance

Remarks:

different programs depending on your exact status, your citizenship, the place where you wish to work, and the type of degree you are aiming for.

Graduate scholarships in the US:

As a general matter, in the USA, you pay to attend a Masters degree program or a professional secondary program (medical school, law school, business school) but you are paid tuition and salary for the entire duration of a PhD program.

Graduate scholarships in the UK:

In the UK, researchers often have little funding for graduate students, and students who apply for their own funding from an independent agency are highly welcome. Universities have tuituion fees for graduate programs which are often vastly different for British, European, and other citizens.
The British Council offers a scholarship database for students wishing to study in Great Britain.
More general information about the financial aspects of living and studying in the UK, as well as links to scholarship possibilities such as Fulbright can be found at the site, http://prospects.ac.uk.